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The Countable Spectrum of Weakly o-minimal Theories of Finite Convexity Rank
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-02-27 DOI: 10.1134/S1064562424702326
B. Sh. Kulpeshov
{"title":"The Countable Spectrum of Weakly o-minimal Theories of Finite Convexity Rank","authors":"B. Sh. Kulpeshov","doi":"10.1134/S1064562424702326","DOIUrl":"10.1134/S1064562424702326","url":null,"abstract":"<p>Here we present a formula counting the countable spectrum of an arbitrary weakly o-minimal theory of finite convexity rank having less than <span>({{2}^{omega }})</span> pairwise non-isomorphic countable models.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 3","pages":"486 - 496"},"PeriodicalIF":0.5,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximate Gyroscope Theory and Its Applications to the Motion of Space Objects
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-02-27 DOI: 10.1134/S1064562424601793
A. G. Petrov
{"title":"Approximate Gyroscope Theory and Its Applications to the Motion of Space Objects","authors":"A. G. Petrov","doi":"10.1134/S1064562424601793","DOIUrl":"10.1134/S1064562424601793","url":null,"abstract":"<p>The motion of an axisymmetric rigid body with a fixed point under the action of a periodic torque is considered. Two small parameters are introduced: one characterizes the smallness of the torque amplitude, and the other characterizes the smallness of the angular momentum component perpendicular to the axis of symmetry. The smallness of the latter parameter usually underlies the approximate theory of gyroscopes. Using this approximation, one can quite simply find the precession velocity of a top under the action of a small periodic torque. It is shown that the relative accuracy of the velocity calculated in this way is nearly independent of the latter small parameter, which does not exceed a value of the order of unity. In this way, a simple formula is found for the precession of an Earth satellite under the action of the Earth’s gravity field. Additionally, a simple formula for the lunisolar precession rate of the Earth’s axis is derived, which agrees well with astronomical observations.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 3","pages":"497 - 499"},"PeriodicalIF":0.5,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Infobusiness As a New Digital Phenomenon in the Socio-Economic Sphere of Russia: Possibilities of Modeling and Regulation
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-01-10 DOI: 10.1134/S1064562424601926
A. S. Voronov, L. N. Orlova, M. V. Shamolin
{"title":"Infobusiness As a New Digital Phenomenon in the Socio-Economic Sphere of Russia: Possibilities of Modeling and Regulation","authors":"A. S. Voronov,&nbsp;L. N. Orlova,&nbsp;M. V. Shamolin","doi":"10.1134/S1064562424601926","DOIUrl":"10.1134/S1064562424601926","url":null,"abstract":"<p>Digital technologies are known to have high potential for economic growth and to promote social and political communications. They are platforms for implementing new business ideas. A new digital phenomenon—information business, or infobusiness—is investigated in the article. How does information business affect the economy and society? This question determines the main topic of discussion. The following methods are used in the article: system analysis, content analysis, sociological survey, comparative analysis, cluster analysis, fuzzy logic methods, and mathematical modeling. The purpose of the article is to determine the relationship and spread of new digital technologies and phenomena in the socio-economic and political spheres of Russia. We propose recommendations on the transformation of socio-economic relations and on modeling and state regulation of processes in the information environment. Additionally, mathematical methods for studying the tasks are proposed.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"421 - 431"},"PeriodicalIF":0.5,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modal Logics of Almost Sure Validities and Zero-One Laws in Horn Classes
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-01-10 DOI: 10.1134/S1064562424601446
V. V. Sliusarev
{"title":"Modal Logics of Almost Sure Validities and Zero-One Laws in Horn Classes","authors":"V. V. Sliusarev","doi":"10.1134/S1064562424601446","DOIUrl":"10.1134/S1064562424601446","url":null,"abstract":"<p>In this paper we develop a method to study Horn classes of Kripke frames from a probabilistic perspective. We consider the uniform distribution on the set of all <i>n</i>-point Kripke frames. A formula is almost surely valid in a Horn class <span>(mathcal{F})</span> if the probability that it is valid in the <span>(mathcal{F})</span>-closure of a random <i>n</i>-point frame tends to 1 as <span>(n to infty .)</span> Such formulas constitute a normal modal logic. We show that for pseudotransitive and pseudo-Euclidean closures this logic equals <b>S5</b>, and the zero-one law holds.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"442 - 449"},"PeriodicalIF":0.5,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Comparison of the Costs of Generating Tollmien–Schlichting Waves and Optimal Disturbances by Optimal Blowing–Suction
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-01-10 DOI: 10.1134/S1064562424601471
K. V. Demyanko, Yu. M. Nechepurenko, I. G. Chechkin
{"title":"Comparison of the Costs of Generating Tollmien–Schlichting Waves and Optimal Disturbances by Optimal Blowing–Suction","authors":"K. V. Demyanko,&nbsp;Yu. M. Nechepurenko,&nbsp;I. G. Chechkin","doi":"10.1134/S1064562424601471","DOIUrl":"10.1134/S1064562424601471","url":null,"abstract":"<p>The problem of generating Tollmien–Schlichting waves (leading eigenmodes) and optimal disturbances with a given accuracy using optimal blowing–suction is considered with the example of Poiseuille flow in a duct of square cross section and streamwise-harmonic blowing–suction through the duct walls. The problem is reduced to solving optimal control problems for the linearized governing equations of viscous incompressible media. It is shown for the first time that generating the optimal disturbances using blowing–suction is much more expensive than generating the leading modes.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"412 - 415"},"PeriodicalIF":0.5,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Stability of Strict Equilibrium of Plasma in Two-Dimensional Mathematical Models of Magnetic Traps
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-01-10 DOI: 10.1134/S1064562424601653
K. V. Brushlinskii, V. V. Kriuchenkov, E. V. Stepin
{"title":"On the Stability of Strict Equilibrium of Plasma in Two-Dimensional Mathematical Models of Magnetic Traps","authors":"K. V. Brushlinskii,&nbsp;V. V. Kriuchenkov,&nbsp;E. V. Stepin","doi":"10.1134/S1064562424601653","DOIUrl":"10.1134/S1064562424601653","url":null,"abstract":"<p>Known from previous works, instabilities in a two-dimensional mathematical model of plasma configuration equilibrium are analyzed using a Galatea-belt toroidal magnetic trap straightened into a cylinder and possessing plane symmetry. It is established that the previously observed large values of the two-dimensional perturbation velocity in the plane of the cylinder cross section arise at the periphery of the configuration near its conventional boundary. They do not grow with time and are caused by arbitrarily small values of density, which is not determined by the idealized model of strict equilibrium. By varying the density, it is possible to influence stability. Three-dimensional (corrugated along the axis of the cylinder) perturbations grow with time in accordance with traditional Lyapunov instability. The dependence of its quantitative characteristics on problem parameters is determined in calculations.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"408 - 411"},"PeriodicalIF":0.5,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Study of the Bias in Monte Carlo N-Particle Estimates for Problems with Particle Interaction
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-01-10 DOI: 10.1134/S1064562424601513
G. A. Mikhailov, G. Z. Lotova, S. V. Rogasinsky
{"title":"Study of the Bias in Monte Carlo N-Particle Estimates for Problems with Particle Interaction","authors":"G. A. Mikhailov,&nbsp;G. Z. Lotova,&nbsp;S. V. Rogasinsky","doi":"10.1134/S1064562424601513","DOIUrl":"10.1134/S1064562424601513","url":null,"abstract":"<p>For a model with interaction of particle trajectories, we justify theoretically and numerically that the <i>N</i>-particle statistical estimates of functionals of the solution to nonlinear kinetic equations have a bias of <span>(O(1{text{/}}N))</span> order. An estimate of the coefficient in the corresponding bias formula is obtained.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"416 - 420"},"PeriodicalIF":0.5,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Numerical Beamforming for Acoustic Source Identification Based on Supercomputer Simulation Data
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-01-10 DOI: 10.1134/S1064562424601550
G. M. Plaksin, T. K. Kozubskaya, I. L. Sofronov
{"title":"On Numerical Beamforming for Acoustic Source Identification Based on Supercomputer Simulation Data","authors":"G. M. Plaksin,&nbsp;T. K. Kozubskaya,&nbsp;I. L. Sofronov","doi":"10.1134/S1064562424601550","DOIUrl":"10.1134/S1064562424601550","url":null,"abstract":"<p>The method of numerical beamforming for processing space-time data obtained in supercomputer simulation of aeroacoustics problems is used to localize a distributed acoustic source formed by the interaction of turbulent flow and aircraft or its elements in flight mode and to determine its amplitude-frequency characteristics. Mathematically, the proposed method is based on solving the inverse problem of determining the right-hand side in the Helmholtz equation for sources of monopole and dipole types. Compared to its analogue intended to analyze experimental measurements, the new method has significant advantages and allows a generalization to correlated sources. The capabilities of the method are demonstrated by solving the problem of identifying an acoustic source generated by a straight aircraft wing with deployed high-lift devices in landing mode.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"435 - 441"},"PeriodicalIF":0.5,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Infinite Algebraic Independence of Polyadic Series with Periodic Coefficients
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-01-10 DOI: 10.1134/S1064562424702296
V. G. Chirskii
{"title":"Infinite Algebraic Independence of Polyadic Series with Periodic Coefficients","authors":"V. G. Chirskii","doi":"10.1134/S1064562424702296","DOIUrl":"10.1134/S1064562424702296","url":null,"abstract":"<p>Consider sequences of integers <span>(a_{n}^{{(k,j)}})</span>, <span>(k = 1, ldots ,{{T}_{j}})</span>, <span>(j = 1, ldots ,m)</span>, such that <span>(a_{n}^{{(k,j)}} = a_{{n + {{T}_{j}}}}^{{(k,j)}})</span>, <span>(j = 1, ldots ,m)</span>, <span>(k = 1, ldots ,{{T}_{j}})</span>, <span>(n = 0,1, ldots )</span>, and consider the series <span>({{F}_{{j,k}}}(z) = sumnolimits_{n = 0}^infty a_{n}^{{(k,j)}}n!{{z}^{n}})</span>, <span>(k = 1, ldots ,{{T}_{j}})</span>, <span>(j = 1, ldots ,m)</span>. The conditions are established under which the set of series <span>({{F}_{{j,k}}}(z))</span>, <span>(k = 2, ldots ,{{T}_{j}})</span>, <span>(j = 1, ldots ,m)</span> and the Euler series <span>(Phi (z) = sumnolimits_{n = 0}^infty n!{{z}^{n}})</span> are algebraically independent over <span>(mathbb{C}(z))</span> and, for any algebraic integer <span>(gamma ne 0)</span>, their values at the point <span>(gamma )</span> are infinitely algebraically independent.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"432 - 434"},"PeriodicalIF":0.5,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Real-Valued Spectral Shift Functions for Contractions and Dissipative Operators
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-11-11 DOI: 10.1134/S1064562424601203
M. M. Malamud, H. Neidhardt, V. V. Peller
{"title":"Real-Valued Spectral Shift Functions for Contractions and Dissipative Operators","authors":"M. M. Malamud,&nbsp;H. Neidhardt,&nbsp;V. V. Peller","doi":"10.1134/S1064562424601203","DOIUrl":"10.1134/S1064562424601203","url":null,"abstract":"<p>In recent joint papers the authors of this note solved a famous problem remained open for many years and proved that for arbitrary contractions with trace class difference there exists an integrable spectral shift function, for which an analogue of the Lifshits–Krein trace formula holds. Similar results were also obtained for pairs of dissipative operators. Note that in contrast with the case of self-adjoint and unitary operators it may happen that there is no <i>real-valued</i> integrable spectral shift function. In this note we announce results that give sufficient conditions for the existence of an integrable real-valued spectral shift function in the case of pairs of contractions. We also consider the case of pairs of dissipative operators.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"399 - 403"},"PeriodicalIF":0.5,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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